{
  "id": "1511.02221",
  "version": "v1",
  "published": "2015-11-06T20:36:36.000Z",
  "updated": "2015-11-06T20:36:36.000Z",
  "title": "On correlations of certain multiplicative functions",
  "authors": [
    "R. Balasubramanian",
    "Sumit Giri",
    "Priyamvad Srivastav"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, the correlation function of the form $\\frac{1}{x}\\sum_{n \\leq x} F(n) G(n-h)$, were $F=f*1$ and $G=g*1$ with $f$ and $g$ small on an average, has been considered. We obtain an estimation formulae for this mean value depending on different order of magnitude of $f$ and $g$. We compute an average of shifted Euler totient function $\\varphi(n-h)$ over square-free integers $n$ and in general expressions of the type $\\sum_{n \\leq x} \\mu^2(n) G(n-h)$, where $G$ is close to $1$ on primes. For certain cases where $f$ and $g$ are small, we make some improvements in the error terms of the corresponding estimations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-06T20:36:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37"
    ],
    "keywords": [
      "multiplicative functions",
      "shifted euler totient function",
      "estimation formulae",
      "mean value",
      "correlation function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151102221B"
    }
  }
}